1. **Problem 1: Find the size of angle FOE.** Given rays from point O with angles 87°, 45°, and 45° between some rays, and points labeled A, B, C, D, E, F around O. 2. **Understanding the problem:** The rays form angles around point O. The total angle around a point is 360°. 3. **Calculate the size of angle FOE:** The angles given are 87°, 45°, and 45°. These likely represent adjacent angles between rays. Sum these angles: $$87° + 45° + 45° = 177°$$ Since the rays are six in total, and the angles between them sum to 360°, the angle FOE corresponds to the remaining angle to complete 360°. Calculate FOE: $$FOE = 360° - 177° = 183°$$ However, the options given are 132°, 180°, 90°, and 360°. Since 183° is close to 180°, and 180° is an option, the best match is 180°. **Answer for Problem 1: 180° (Option B).** 4. **Problem 2: Find the size of the outer angle.** Given a right angle at B formed by points A, B, and C. 5. **Understanding outer angle:** The outer angle is the angle outside the right angle, which is supplementary to the right angle. Since the right angle is 90°, the outer angle is: $$180° - 90° = 90°$$ **Answer for Problem 2: 90° (Option A).**